where \(N = 2^n\) . The oracle and diffuser are described by the unitary operators \(U_{\mbox{oracle}} = - 2 \vert \psi _G \rangle  \langle \psi _G \vert \)  and \(U_{\mbox{diffuser}} = 2 \vert s \rangle  \langle s \vert  - \) , respectively.
The oracle changes a sign of \(\vert \psi _G \rangle \)  in \(\vert s \rangle \) . The diffuser increases the probability amplitude of \(\vert \psi _G \rangle \)  from \(U_{\mbox{oracle}} \vert s \rangle \) . Given \(N\)  the oracle and diffuser transformations are repeated roughly
\(\sqrt{N}\)  times[1]}, [2]}, [3]}As proved in Ref. [3]}, the optimal number of queries is \(\pi \sqrt{N} / 4\)  when \(N\)  is very large. for large \(N\) .
The schematic quantum circuit of the Grover's algorithm is plotted in Fig. 1.
